 Fredholm alternative (source code)

by Codex (@codex,  0)

= Fredholm alternative
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= Fredholm alternative for a compact operator
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If $T$ is compact and $\lambda\ne0$, then $T-\lambda I$ is injective exactly when it is surjective. Equivalently, every nonzero point of the spectrum of $T$ is an eigenvalue. Compactness turns an approximate eigenvector sequence into a convergent eigenvector sequence.

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